Numerical Simulations of Scattering Experiments

Abstract

A special numerical realization of a T-matrix method in Cartesian coordinates was already discussed in Chap. 6 in conjunction with Rayleigh’s hypothesis. It was applied there, not to calculate the scattering quantities in the far-field but to obtain the scattered near-field generated by a plane wave perpendicularly incident on an ideal metallic and periodic grating. Now, we intend to present the far-field scattering properties of single nonspherical but rotationally symmetric scatterers in spherical coordinates. This will be realized again by applying a T-matrix method. The restriction to rotationally symmetric particles results in important numerical simplifications, due to the symmetry relation (4.51) and the independence of the orientation of the Eulerian angle γ. But despite this restriction we will become acquainted with some scattering properties, which are characteristic of nonspherical particles, in general. Regarding spherical scatterers (i.e., Mie theory) there exist already a large number of different numerical methods whose correctness, efficiency, and reliability have been proven in many applications. But regarding nonspherical particles, the situation is much more complicate. The numerical effort increases considerably, and deriving the necessary convergence criteria becomes a much more complex task. The latter depends strongly on the chosen method and requires a lot of experience and a detailed knowledge of its methodical background. Applying a certain method to a new nonspherical scatterer geometry is therefore always a new adventure. Most experiences have been gained over the last decades with rotationally symmetric particles like spheroids, Chebyshev particles, and finite but circular cylinders. This is the essential reason for restricting the following simulations to these geometries. The program mieschka we will present in this chapter, can be applied to other rotationally symmetric geometries, as well. But then, there are possibly only a few or even no results from other methods to compare to. In this situation, one has to throw a critical look upon the outcome of mieschka, and more reasonable tests from a physical point of view may have to be taken into consideration.